The present disclosure relates to change detection from noisy multivariate time-series data.
The task of change detection has a long history in statistics. The standard strategy is to use a parametric model for probability density and compute the likelihood ratio to quantify the degree of change between fitted distributions. FIG. 1 shows a typical setting, where the task is to compute a degree of change, or the change score, of the data within the test window taken at time t in comparison to the training window.
When applying a change detection method to real-world problems, interpretability and robustness to nuisance noise variables are important considerations. To validate detected changes with domain knowledge, it is almost always required to explicitly present statistics (or feature) for the parametric model, such as the mean for Gaussian. Although it is possible to design an algorithm that skips the explicit step of feature extraction and jumps directly into score calculation, such an approach suffers from a lack of interpretability. In the multivariate setting, the robustness to noise variables is also important, since changes may not always occur in all of the variables simultaneously. Under the existence of nuisance noise variables, the performance of direct density-ratio estimation approaches is known to significantly degrade.